International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F. ch. 19.4, pp. 440-441   | 1 | 2 |

Section 19.4.3.3. Relationship of contrasting regions

D. M. Engelmana* and P. B. Mooreb

aDepartment of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520, USA, and  bDepartments of Chemistry and Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520, USA
Correspondence e-mail:  don@paradigm.csb.yale.edu

19.4.3.3. Relationship of contrasting regions

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Where a particle has two regions of different scattering density, the square of the total observed radius of gyration, [R_{T}^{2}], can be obtained as the weighted sum of squares of the two individual radii, [R_{1}^{2}] and [R_{2}^{2}], and the square of the distance between the centres of scattering mass of the two regions, [d_{12}^{2}], as [R_{T}^{2} = f_{1}R_{1}^{2} + f_{2}R_{2}^{2} + f_{1}f_{2}d_{12}^{2}, \eqno(19.4.3.8)] where the f's are the fractions of the total scattering from each of the two regions at the solvent contrast being used in the experiment (Moore et al., 1974[link]). By varying the contrast, a set of differently weighted equations can be obtained, from which the individual radii and the separation can be derived. This method is an alternative to the Stuhrmann analysis described above. An example of the use of this approach, based formally on the parallel axis theorem of mechanics, is found in studies of the ribosome (Moore et al., 1974[link]). An alternative that has proved useful is to combine neutron and X-ray scattering data, since the weighting factors will differ for distinct regions, such as the RNA and protein components of the ribosome (Serdyuk et al., 1979[link]).

References

First citation Moore, P. B., Engelman, D. M. & Schoenborn, B. P. (1974). Asymmetry in the 50S ribosomal subunit of Escherichia coli. Proc. Natl Acad. Sci. USA, 71, 172–176.Google Scholar
First citation Serdyuk, I. N., Grenader, A. K. & Zaccai, G. (1979). Study of the internal structure of E. coli ribosomes by neutron and X-ray scattering. J. Mol. Biol. 135, 691–707.Google Scholar








































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